Transcript Parallel and Perpendicular Lines

Parallel and Perpendicular
Lines
Parallel and Perpendicular Lines
• Perpendicular lines are two lines that
intersect to form a 90º angle
•
Parallel and Perpendicular Lines
• Parallel lines are two lines that, if extended
indefinitely, would never cross or touch
• In the figure below, line l is parallel to line m
• l ll m
l
m
Parallel and Perpendicular Lines
Checkpoint
• Name all pairs of parallel line segments in
each of the figures below:
AB ll DC, AD ll BC, and EH ll FG
a
b
e
f
d
c
h
g
Parallel and Perpendicular Lines
Checkpoint
• Name all pairs of perpendicular line
segments in each of the figures below:
AD DC, DC BC, AB BC, AB AD, EH GH, and GH FG
a
b
e
f
d
c
h
g
Transversals
• A line that intersects two other lines is called a
transversal
• In the figure below, l || m and n is the transversal
• Eight angles are formed when a transversal
intersects two parallel lines
1
2
4
l
3
5
8
m
6
7
n
Transversal Mini-Lab
For this mini-lab, you will need:
• Notebook paper
• Pencil
• Two colored pencils (share with neighbor)
• Ruler (share with neighbor)
• Protractor
Transversal Mini-Lab
1.
2.
3.
Draw two parallel lines using the lines on your
notebook paper.
Using a ruler, draw any line (not perpendicular) to
intersect these two parallel lines.
Label the angles formed using the numbers 1 – 8 as
shown below:
1
2
4
l
3
5
8
m
6
7
n
Transversal Mini-Lab
4.
5.
6.
7.
Use a protractor to measure each angle and record it’s
measurement below the figure (example: m 2 = 28º)
Shade angle 1 and each angle that has a congruent
measurement with a colored pencil.
Shade angle 2 and each angle that has a congruent
measurement with another colored pencil.
Compare your results with a neighbor and be prepared
to discuss
Transversal Mini-Lab
(what do you already know?)
•
Angles 1 and 2 are supplementary
angles and must equal 180º
1
2
4
l
3
5
8
m
6
7
n
Transversal Mini-Lab
(what do you already know?)
•
Angles 1 and 3 and angles 2 and 4 are
vertical angles that have the same
measure.
1
2
4
l
3
5
8
m
6
7
n
Congruent Angles with Parallel
Lines
•
•
The symbol
means congruent to
If a pair of parallel lines is intersected by
a transversal, pairs of congruent angles
are formed
1
2
4
l
3
5
6
8
m
7
n
Congruent Angles with Parallel
Lines
•
•
Congruent angles formed in between the
parallel lines are known as alternate
interior angles
4
6 and
3
5
1
2
4
l
3
5
6
8
m
7
n
Congruent Angles with Parallel
Lines
•
•
Congruent angles formed outside of the
parallel lines are known as alternate
exterior angles
1
7 and
2
8
1
2
4
l
3
5
6
8
m
7
n
Congruent Angles with Parallel
Lines
•
•
Congruent angles formed in the same position on the
two parallel lines in relation to the transversal are
known as corresponding angles
1
5;
2
6;
3
1
7; and
2
4
6
8
8
l
3
5
4
m
7
n
Congruent Angles with Parallel
Lines Checkpoint
• In the figure below, m 1 = 65
• Explain how you find the measure of each of the
rest of the angles using vocabulary words such
as supplementary, vertical, corresponding,
alternate interior, and alternate exterior angles
n
1
2
4
5
8
l
3
6
7
m
Congruent Angles with Parallel
Lines Checkpoint
n
1
2
4
5
8
l
3
6
7
m
Angle
Measure
Concept
1
65°
Given
2
115°
Supplementary with 1
3
65°
Vertical with 1
4
115°
Vertical with 2
5
65°
Corresponding with 1, Alt. Interior with 3
6
115°
Corresponding with 2, Alt. Interior with 4
7
65°
Corresponding with 3, Alt. Exterior with 1, Vertical with 5
8
115°
Corresponding with 4, Alt. Exterior with 2, Vertical with 6
Congruent Angles with Parallel
Lines and Equations
• In the figure below, m 1 = 11x
• m 6 = 5x + 100
• Find the value of x and then find the measure of
the remaining angles
Hint: Angles 2 and 6 are Corresponding
and angles 1 and 2 are Supplementary
1
2
4
3
5
8
l
6
7
m
n
Congruent Angles with Parallel
Lines and Equations
1 = 11x°,
6 = 5x° + 100°
11x° + 5x° + 100° = 180°
16x° + 100° = 180°
-100° -100°
16x° = 80°
16
16
x° = 5°
1 + 2 = 180°
n
1
2
4
5
8
Angle
Measure
1
55°
Supplementary with 6, 11(5) = 55
2
125°
Corresponding with 6
3
55°
Vertical with 1
4
125°
Vertical with 2
5
55°
Corresponding with 1, Alt. Interior with 3
6
125°
Supplementary with 1, 5(5) + 100 = 125
7
55°
Corresponding with 3, Alt. Exterior with 1, Vertical with 5
8
l
125°
3
6
7
m
Concept
Corresponding with 4, Alt. Exterior with 2, Vertical with 6
Homework
• Skill 2: Parallel and Perpendicular Lines
(both sides)
• Practice 6-1: Line and Angle Relationships
(both sides)